De Alfaro and Henzinger’s Interface Automata (IA) and Nyman et al.’s recent combination IOMTS of IA and Larsen’s Modal Transition Systems (MTS) are established frameworks for specifying interfaces of system components. However, neither IA nor IOMTS consider conjunction that is needed in practice when a component satisfies multiple interfaces, while Larsen’s MTS-conjunction is not closed. In addition, IOMTS-parallel composition exhibits a compositionality defect.This paper defines conjunction on IA and MTS and proves the operators to be ‘correct’, i.e., the greatest lower bounds wrt. IA- and resp. MTS-refinement. As its main contribution, a novel interface theory called Modal Interface Automata (MIA) is introduced: MIA is a rich subset of IOMTS, is equipped with compositional parallel and conjunction operators, and allows a simpler embedding of IA than Nyman’s. Thus, it fixes the shortcomings of related work, without restricting designers to deterministic interfaces as Raclet et al.’s modal interface theory does.